In the field of wireless digital communications, a digital signal to be transmitted is modulated and filtered before being transmitted. Traditionally, a first shaping filter is applied to a modulated signal before it is transmitted by radio and a second shaping filter, adapted to suit the first filter, is applied to the signal received by a receiver before it is demodulated.
The shaping filter, applied on transmission, and the adapted filter, applied at reception, need to be compliant with precise spectrum templates meeting numerous constraints. Moreover, the interference between symbols that is associated with the filters needs to be limited so as not to degrade the performances of the demodulation. Moreover, for linear modulations, the ratio between the peak power and the average power needs to be as low as possible in order to allow transmission at an optimum power.
In order to observe all these constraints and obtain good transmission performance, the usual method involves using root raised-cosine filters. These filters have the suitable properties that are required for shaping filters, notably because they allow observance of the Nyquist criterion, which ensures almost total elimination of the interference between symbols.
However, root raised-cosine filters preserve their beneficial properties only when they are synthesized with a large number of coefficients. The reason is that the truncation of the filter to a reduced number of coefficients decreases the frequency selectivity of the filter.
Now, when the capacity of the processor that executes the shaping filtering is limited, the use of filters of great length is prohibited. Even for processors having higher computation capacities, the filtering operation often continues to be an operation that is complex to perform, the complexity being directly proportional to the length of the filter.
There is therefore a need to synthesize shaping filters of short length, that is to say having a small number of coefficients.
One alternative to improve performance involves applying a weighting window to the truncated filter, for example a Blackman window or a Hamming window, but this method generates interference between symbols.
The technical problem that the present invention aims to solve is thus that of finding a method for synthesizing shaping filters that allows the assured production of filters having good properties in terms of interference between symbols and crest factor despite their limited length.
Methods for synthesizing digital filters that are suited to shaping signals to be transmitted are notably described in the patent application publications EP 0441732 and WO 2000065790.
These solutions notably have the following drawbacks. The solution proposed in the application EP 0441732 applies only to multicarrier modulations, while the solution proposed in the application WO 2000065790 requires the use of a particular windowing function.